Hmmmm. I never would have thought to check the handlebar stem & clamp as HillRider suggested. If you think about the way you grip the bars while standing & with each pedal stroke I think your weight shifts slightly from side to side and your grip on the handlebars provides some amount of torque. Not sure of the exact physics, but it makes sense to check those too, along with the other aspects mentioned. Interestd to hear what the OP finds.